The paper addresses the problem of efficient identification of the Open Circuit Voltage versus State of Charge (OCV-SOC) dependency for lithium-ion batteries, which is a critical step for creating accurate Battery Management Systems (BMS). Traditional approaches using uniform discretization are characterized by increased time costs and low accuracy, since they do not take into account the shape of the OCV(SOC) curve. This article presents four adaptive discretization algorithms based on local function nonlinearity analysis: second derivative calculation, moving window regression analysis, collinearity analysis via triangle area, and tangent angle variance analysis. The theoretical basis of the developed methods is the principle of interpolation error equidistribution, linking the discretization step to the local function curvature. Numerical simulation was performed using a battery mathematical model with a second-order Thevenin equivalent circuit. Results demonstrate that the proposed algorithms provide approximation accuracy comparable to a fine uniform grid (2 % SOC step). The methods based on the second derivative and regression analysis showed the highest efficiency regarding the accuracy-to-time ratio. The developed approaches include smoothing mechanisms to ensure robustness against measurement noise and are recommended for optimizing battery characterization processes in research and industrial conditions.
This paper studies the production of D∗-mesons in deep inelastic scattering of electrons on protons within the framework of the leading approximation in the strong coupling constant in the collinear parton model and in the parton Reggeization approach. The hadronization of c-quarks is described within the Peterson fragmentation model taking into account the masses of c-quarks and D∗-mesons. The calculations were performed using the KaTie parton level generator and unintegrated parton distribution functions in the modified Kimber – Martin – Ryskin – Watt model. It is shown that the experimental data of the ZEUS and H1 collaborations, obtained at energies √s = 300 − −319 GeV, are in satisfactory agreement with theoretical calculations, with the exception of the region of high D∗-meson pseudorapidity. No significant differences are observed in the predictions of the collinear parton model and the parton Reggeization approach. Predictions are made for various differential cross sections for the production of D∗-mesons at the EIC collider energy, √s = 140 GeV.
In this paper, we consider a nonlocal initial-boundary problem. A distinguishing feature of this problem is the form of nonlocal boundary conditions which are known in scientific literature as Steklov conditions. A large proportion of papers dealing with nonlocal problems with Steklov conditions is devoted to second-order parabolic and hyperbolic equations. In the presented here paper we study the nonlocal problem with Steklov boundary conditions for fourth-order equation and obtain sufficient conditions for unique solvability of it in Sobolev space. The proof of both uniqueness and existence of the solution to the problem under consideration is based on a priori estimates and the properties of Sobolev spaces
We establish continuous dependence on parameters and initial conditions, as well as explicit solution estimates, for fractional differential equations involving the Atangana – Baleanu derivative in the Caputo sense (ABC). Despite the existence of analogous results for the Atangana – Baleanu derivative in the Riemann – Liouville sense (ABR) [13], for the Caputo formulation such results have previously been obtained only for systems with generalised Mittag – Leffler kernels [16]. We fill this gap by proving, for scalar ABC equations with standard Mittag – Leffler kernels, a theorem on equivalent integral formulation, an explicit exponential solution estimate, and theorems on continuous dependence with respect to initial data and parameters. The proofs rest on the representation of the ABC derivative via a Prabhakar-type fractional integral, Krasnoselskii’s fixed-point theorem, and the Gronwall – Bellman inequality
This paper identifies the advantages and disadvantages of the subject-methodological and organizational-didactic potential of artificial-intelligence and neural network-technologies (AI-technologies and neural networks). It examines the risks and challenges associated with the implementation of these technologies in the educational process and analyzes the specifics of their application in mathematics and science education. A list of AI-based applications, services, platforms, and programs used in mathematics and science education is provided, along with a didactic model for the formation and development of the subject-digital culture of undergraduate pedagogical students. Using examples of specific tasks solved using AI-tools, the conditions for the productive use of the subject-methodological and organizational-didactic potential of AI-technologies and neural networks in the teaching of mathematics and computer science are determined. Prospects for using AI-tools as auxiliary organizational-didactic tools used by teachers and students in their daily activities are outlined.
